Approximation of the long-term dynamics of the dynamical system generated by the multilayer quasigeostrophic equations of the ocean

2015 ◽  
Vol 32 (3) ◽  
pp. 1041-1065 ◽  
Author(s):  
Theodore Tachim Medjo ◽  
C. Tone ◽  
F. Tone
Keyword(s):  
Dynamical System ◽  
Quasigeostrophic Equations

scholarly journals Geosystemics and Earthquakes

2018 ◽  
Author(s):  
Angelo De Santis ◽  
Gianfranco Cianchini ◽  
Rita Di Giovambattista ◽  
Cristoforo Abbattista ◽  
Lucilla Alfonsi ◽  
...  
Keyword(s):  
Dynamical System ◽  
Solid Earth ◽  
Case Studies ◽  
Central Italy ◽  
Point Of View ◽  
Earth System ◽  
Complex Dynamical System ◽  
The Earth ◽  
Earth’S Interior

Abstract. Geosystemics (De Santis 2009, 2014) studies the Earth system as a whole focusing on the possible coupling among the Earth layers (the so called geo-layers), and using universal tools to integrate different methods that can be applied to multi-parameter data, often taken on different platforms. Its main objective is to understand the particular phenomenon of interest from a holistic point of view. In this paper we will deal with earthquakes, considered as a long term chain of processes involving, not only the interaction between different components of the Earth’s interior, but also the coupling of the solid earth with the above neutral and ionized atmosphere, and finally culminating with the main rupture along the fault of concern (De Santis et al., 2015a). Some case studies (particular emphasis is given to recent central Italy earthquakes) will be discussed in the frame of the geosystemic approach for better understanding the physics of the underlying complex dynamical system.

Markov cellular automata models for chronic disease progression

2015 ◽  
Vol 08 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Jane Hawkins ◽  
Donna Molinek
Keyword(s):  
Dynamical System ◽  
Human Immunodeficiency Virus ◽  
Hepatitis C ◽  
Chronic Conditions ◽  
Chronic Condition ◽  
Physical Significance ◽  
Markov Shifts ◽  
Immunodeficiency Virus ◽  
Long Term Prognosis

We analyze a Markov cellular automaton that models the spread of viruses that often progress to a chronic condition, such as human immunodeficiency virus (HIV) or hepatitis C virus (HCV). We show that the complex dynamical system produces a Markov process at the later stages, whose eigenvectors corresponding to the eigenvalue 1 have physical significance for the long-term prognosis of the virus. Moreover we show that drug treatment leads to chronic conditions that can be modeled by Markov shifts with more optimal eigenvectors.

scholarly journals Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems

1989 ◽  
Vol 31 (1) ◽  
pp. 48-75 ◽  
Author(s):  
A. J. Roberts
Keyword(s):  
Dynamical System ◽  
Invariant Manifold ◽  
Initial Conditions ◽  
Long Term Evolution ◽  
Equation Model ◽  
Starting Position ◽  
System A ◽  
Term Evolution ◽  
Shear Dispersion

AbstractA centre manifold or invariant manifold description of the evolution of a dynamical system provides a simplified view of the long term evolution of the system. In this work, I describe a procedure to estimate the appropriate starting position on the manifold which best matches an initial condition off the manifold. I apply the procedure to three examples: a simple dynamical system, a five-equation model of quasi-geostrophic flow, and shear dispersion in a channel. The analysis is also relevant to determining how best to account, within the invariant manifold description, for a small forcing in the full system.

scholarly journals STABILITY OF NEARLY-INTEGRABLE SYSTEMS WITH DISSIPATION

2013 ◽  
Vol 23 (02) ◽  
pp. 1350036 ◽  
Author(s):  
CHRISTOPH LHOTKA ◽  
ALESSANDRA CELLETTI
Keyword(s):  
Dynamical System ◽  
Vector Field ◽  
Stability Behavior ◽  
Term Stability ◽  
Long Term Stability ◽  
Nearly Integrable Systems ◽  
The Stability ◽  
Two Parameters ◽  
Action Variables

We study the stability of a vector field associated to a nearly-integrable Hamiltonian dynamical system to which a dissipation is added. Such a system is governed by two parameters, namely the perturbing and dissipative parameters, and it depends on a drift function. Assuming that the frequency of motion satisfies some resonance assumption, we investigate the stability of the dynamics, and precisely the variation of the action variables associated to the conservative model. According to the structure of the vector field, one can find linear and long-term stability times, which are established under smallness conditions of the parameters. We also provide some applications to concrete examples, which exhibit a linear or long-term stability behavior.

scholarly journals THE ARCHITECTURE OF A SCHOOL SYSTEM ACCORDING TO THE THEORY OF DYNAMICAL SYSTEMS

2012 ◽  
Vol 46 (1) ◽  
pp. 7-14
Author(s):  
Boris Aberšek ◽  
Janez Bregant
Keyword(s):  
Dynamical System ◽  
School Reform ◽  
School System ◽  
Positive Impact ◽  
Main Idea ◽  
Educational Process ◽  
The Other ◽  
Mathematical Methods ◽  
Societal Expectations

From the experience of recent years it seems clear that the existing educational system, as a whole, is perceived as an ailing system that fails to meet the needs of a major portion of the society it serves. Every aspect of the educational process must be studied and reconsidered in the light of new and different societal expectations. In the last decades we started with one school reform after the other, but it looks now that these changes had no positive impact whatsoever. Even worse, the school system was damaged afterwards. In this paper we will explore some possibilities how to improve it without facing these consequences. The main idea is, as a result of our latest research, that mathematical methods for describing and simulating could be very useful for predicting and simulating school systems without using a long term and complex empirical experimentation. The paper introduces the correlation between the dynamical mathematical calculus and the educational school system and elaborates to some extent the basic idea of using the former to predict the latter. Key words: architecture, mathematical modelling, school system, theory of dynamical system.

scholarly journals CONSTRUCTION OF CHAOTIC DYNAMICAL SYSTEM

2010 ◽  
Vol 15 (1) ◽  
pp. 1-8
Author(s):  
Inese Bula ◽  
Irita Rumbeniece
Keyword(s):  
Dynamical System ◽  
Discrete Dynamical System ◽  
Symbol Space ◽  
Chaotic Dynamical System ◽  
Order Difference ◽  
Chaotic Mapping ◽  
Order Difference Equation ◽  
Unit Segment ◽  
Dynamical System Models

The first‐order difference equation xn+ 1 = f(xn ), n = 0,1,…, where f: R → R, is referred as an one‐dimensional discrete dynamical system. If function f is a chaotic mapping, then we talk about chaotic dynamical system. Models with chaotic mappings are not predictable in long‐term. In this paper we consider family of chaotic mappings in symbol space S 2. We use the idea of topological semi‐conjugacy and so we can construct a family of mappings in the unit segment such that it is chaotic.

Bayesian inference of a dynamical model evaluating Deltamethrin effect on Daphnia survival

2018 ◽  
Vol 2 ◽  
pp. 14
Author(s):  
Abdoulaye Diouf ◽  
Baba Issa Camara ◽  
Diene Ngom ◽  
Hela Toumi ◽  
Vincent Felten ◽  
...  
Keyword(s):  
Dynamical System ◽  
Bayesian Inference ◽  
Environmental Risks ◽  
Real Problem ◽  
Inference Algorithm ◽  
Inference Method ◽  
Toxic Compound ◽  
Bayesian Inference Method ◽  
Long Term Impact

The estimation of toxicokinetic and toxicodynamic (TK-TD) models parameters is a real problem in research. These models highlight a dynamics of  internalisation of a toxic compound and a dynamics of the damage that this contaminant will cause on an organism and of possible repairs on the latter. This coupling TK-TD makes it possible to connect these measurements at different times with the same set of parameters sometimes very important in number. In this paper, the focus is on assessing the long-term impact of deltamethrin effects on a sample of daphnia magna survival. For this purpose we fit our TK-TD model of deltamethrin bio-accumuluation and daphnia survival to our experimental data by using bayesian inference algorithm developed in the package deBinfer of R. This bayesian inference method allows estimate simultaneously all the parameters of deltamethrin bio-accumuluation and daphnia survival dynamical system. For the estimation of the environmental risks, our results show that whatever the concentration or duration of exposure, the concentration of bioaccumulated deltamerin should not exceed on average 6.188 ng/L, at the risk of observing the deadly effects

Dynamics of Two-Sided Markets

2016 ◽  
Vol 14 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Victoria Rayskin
Keyword(s):  
Dynamical System ◽  
Higher Dimensions ◽  
Natural Generalization ◽  
Long Term Behavior ◽  
Two Sided Markets

AbstractThis paper considers a dynamical system, which models a two-sided market. I evaluate the volume of users from each side of the market as a function of time. I formulate and prove theorems describing the long-term behavior and tendency of the market. Even though I consider generic attachment functions, I obtain a concrete result, formulated in terms of properties of attachment functions. This result is followed by examples (defined by the most popular in economics attachment functions), which illustrate behavior of the two-sided markets. I also simulate some two-sided market scenarios, showing how adjustments of attachment functions can influence the users’ dynamics. The dynamical system’s approach to the study of two-sided market problem allows natural generalization to multi-sided market, where one can utilize the same technique and obtain similar results in higher dimensions.

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